# zbMATH — the first resource for mathematics

## Tate, John Torrence jun.

Compute Distance To:
 Author ID: tate.john-torrence Published as: Tate, J.; Tate, J. T.; Tate, John; Tate, John T.; Tate, John Torrence Homepage: http://www.ma.utexas.edu/text/webpages/tate.html External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND · MacTutor Awards: Wolf Prize (2003) · Abel Prize (2010) Member of Collective: Bourbaki, Nicolas
 Documents Indexed: 100 Publications since 1951, including 15 Books Biographic References: 15 Publications
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#### Co-Authors

 53 single-authored 9 Artin, Michael 7 Mazur, Barry 4 Artin, Emil 3 Mumford, David Bryant 3 Serre, Jean-Pierre 3 Van den Bergh, Michel 2 Atiyah, Michael Francis 2 Bass, Hyman 2 Cartier, Pierre 2 Ferrer Santos, Walter Ricardo 2 Jackson, Allyn 2 Katz, Nicholas Michael 2 Lang, Serge 2 Lubin, Jonathan D. 2 Moskowitz, Martin A. 2 Oort, Frans 2 Schelter, William F. 2 Silverman, Joseph Hillel 1 Bateman, Paul Trevier 1 Bergman, George M. 1 Brauer, Richard 1 Deligne, Pierre René 1 Demazure, Michel 1 Fröhlich, Albrecht 1 Gerstenhaber, Murray 1 Goldfeld, Dorian Morris 1 Gowers, William Timothy 1 Greenberg, Marvin Jay 1 Hartshorne, Robin 1 Illusie, Luc 1 Jones, Peter Wilcox 1 Jordan, Bruce W. 1 Jorgenson, Jay Alan 1 Kawada, Yukiyosi 1 Keeton, Allan G. 1 Kleiman, Steven Lawrence 1 Kostant, Bertram 1 Ladegaillerie, Yves 1 Lichtenbaum, Stephen 1 Lochak, Pierre 1 Magid, Andy Roy 1 Mattuck, Arthur 1 Messing, William 1 Moore, Calvin C. 1 Mostow, George Daniel 1 Murre, Jacob P. 1 Nahlus, Nazih 1 Poonen, Bjorn 1 Rains, Eric M. 1 Ramakrishnan, Dinakar 1 Ribet, Kenneth Alan 1 Rodriguez-Villegas, Fernando 1 Rosset, Shmuel 1 Schneps, Leila 1 Schwartz, James M. 1 Sen, Shankar 1 Shafarevich, Igor’ Rostislavovich 1 Shepherd-Barron, Nicholas Ian 1 Smith, S. Paul 1 Stein, William A. 1 Teitelbaum, Jeremy T. 1 Tisseyre, François 1 Voloch, José Felipe
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#### Serials

 8 Inventiones Mathematicae 4 Notices of the American Mathematical Society 4 Annals of Mathematics. Second Series 3 American Journal of Mathematics 3 Progress in Mathematics 2 Communications on Pure and Applied Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Duke Mathematical Journal 2 Journal für die Reine und Angewandte Mathematik 2 Proceedings of the American Mathematical Society 2 Science 2 Undergraduate Texts in Mathematics 2 Springer VideoMATH 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Advances in Mathematics 1 Bulletin de la Société Mathématique de France 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Illinois Journal of Mathematics 1 Journal of the Faculty of Science. Section I A 1 The Journal of the Indian Mathematical Society. New Series 1 Journal of the Mathematical Society of Japan 1 Nagoya Mathematical Journal 1 Soviet Mathematics. Doklady 1 Topology 1 $$K$$-Theory 1 IMRN. International Mathematics Research Notices 1 L’Enseignement Mathématique. 2e Série 1 Bulletin of the American Mathematical Society. New Series 1 Izvestiya: Mathematics 1 Documenta Mathematica 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Colloques Internationaux du Centre National de la Recherche Scientifique
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#### Fields

 44 Number theory (11-XX) 42 Algebraic geometry (14-XX) 15 History and biography (01-XX) 7 Field theory and polynomials (12-XX) 7 Associative rings and algebras (16-XX) 5 General and overarching topics; collections (00-XX) 4 Commutative algebra (13-XX) 4 Nonassociative rings and algebras (17-XX) 3 $$K$$-theory (19-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX)

#### Citations contained in zbMATH

82 Publications have been cited 3,890 times in 3,140 Documents Cited by Year
Good reduction of abelian varieties. Zbl 0172.46101
Serre, Jean-Pierre; Tate, J.
1968
Endomorphisms of Abelian varieties over finite fields. Zbl 0147.20303
Tate, J.
1966
Algorithm for determining the type of a singular fiber in an elliptic pencil. Zbl 1214.14020
Tate, J.
1975
Relations between $$K_2$$ and Galois cohomology. Zbl 0359.12011
Tate, John
1976
Some algebras associated to automorphisms of elliptic curves. Zbl 0744.14024
Artin, M.; Tate, J.; Van den Bergh, M.
1990
On $$p$$-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Zbl 0699.14028
Mazur, B.; Tate, J.; Teitelbaum, J.
1986
Modules over regular algebras of dimension 3. Zbl 0763.14001
Artin, M.; Tate, J.; Van den Bergh, M.
1991
Homology of Noetherian rings and local rings. Zbl 0079.05501
Tate, John
1957
Class field theory. Reprint of the 1990 2nd ed. Zbl 1179.11040
Artin, Emil; Tate, John
2009
Number theoretic background. Zbl 0422.12007
Tate, J.
1979
Group schemes of prime order. Zbl 0195.50801
Tate, John; Oort, Frans
1970
Rational points on elliptic curves. Zbl 0752.14034
Silverman, Joseph H.; Tate, John
1992
$$p$$-divisible groups. Zbl 0157.27601
Tate, J. T.
1967
The arithmetic of elliptic curves. Zbl 0296.14018
Tate, John T.
1974
Formal complex multiplication in local fields. Zbl 0128.26501
Lubin, Jonathan; Tate, John
1965
Rigid analytic spaces. Zbl 0212.25601
Tate, J.
1971
Class field theory. Zbl 0176.33504
Artin, Emil; Tate, John
1968
Algebraic cycles and poles of zeta functions. Zbl 0213.22804
Tate, John T.
1965
The Stark conjectures on Artin $$L$$-functions at $$s=0$$. Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher. Zbl 0545.12009
Tate, John
1984
The Milnor ring of a global field. Zbl 0299.12013
Bass, H.; Tate, J.
1973
Quantum deformations of $$\text{GL}_ n$$. Zbl 0753.17015
Artin, Michael; Schelter, William; Tate, John
1991
Nilpotent quotient groups. Zbl 0125.01503
Tate, J.
1964
Principal homogeneous spaces over Abelian varieties. Zbl 0097.36203
Lang, Serge; Tate, John
1958
Formal moduli for one-parameter formal Lie groups. Zbl 0156.04105
Lubin, J.; Tate, J.
1966
On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. Zbl 0199.55604
Tate, John
1966
Homological properties of Sklyanin algebras. Zbl 0876.17010
Tate, John; Van den Bergh, Michel
1996
Residues of differentials on curves. Zbl 0159.22702
Tate, John
1968
Genus change in inseparable extensions of function fields. Zbl 0047.03901
Tate, John
1952
Global class field theory. Zbl 1179.11041
Tate, J. T.
1967
Duality theorems in Galois cohomology over number fields. Zbl 0126.07002
Tate, J.
1963
Conjectures on algebraic cycles in $$\ell$$-adic cohomology. Zbl 0814.14009
Tate, John
1994
The cohomology groups of tori in finite Galois extensions of number fields. Zbl 0146.06501
Tate, J.
1966
Class field theory. 2nd ed. Zbl 0681.12003
Artin, Emil; Tate, John
1990
Refined conjectures of the “Birch and Swinnerton-Dyer type”. Zbl 0636.14004
Mazur, B.; Tate, J.
1987
Classes d’isogénie des variétés abéliennes sur un corps fini (d’après Z. Honda). Zbl 0212.25702
Tate, John
1971
Canonical height pairings via biextensions. Zbl 0574.14036
Mazur, B.; Tate, J.
1983
On the characters of finite groups. Zbl 0065.01401
Brauer, Richard; Tate, John
1955
A note on finite ring extensions. Zbl 0043.26701
Artin, Emil; Tate, John T.
1951
The non-existence of certain Galois extensions of $$\mathbb{Q}$$ unramified outside 2. Zbl 0814.11057
Tate, John
1994
Points of order 13 on elliptic curves. Zbl 0268.14009
Mazur, B.; Tate, J.
1973
The $$p$$-adic sigma function. Zbl 0735.14020
Mazur, B.; Tate, J.
1991
A reciprocity law for $$K_2$$-traces. Zbl 0514.18010
Rosset, Shmuel; Tate, John
1983
The rank of elliptic curves. Zbl 0168.42201
Tate, J. T.; Shafarevich, I. R.
1967
The higher dimensional cohomology groups of class field theory. Zbl 0047.03703
Tate, John
1952
On the Jacobians of plane cubics. Zbl 1092.14054
Artin, Michael; Rodriguez-Villegas, Fernando; Tate, John
2005
Variation of the canonical height of a point depending on a parameter. Zbl 0618.14019
Tate, J.
1983
WC-groups over $$p$$-adic fields. Zbl 0091.33701
Tate, J.
1958
The center of the $$3$$-dimensional and $$4$$-dimensional Sklyanin algebras. Zbl 0809.16053
Smith, S. P.; Tate, J.
1994
Computation of $$p$$-adic heights and log convergence. Zbl 1135.11034
Mazur, Barry; Stein, William; Tate, John
2007
Symbols in arithmetic. Zbl 0229.12013
Tate, John
1971
Rational points on elliptic curves. 2nd ed. Zbl 1346.11001
Silverman, Joseph H.; Tate, John T.
2015
A review of non-Archimedean elliptic functions. Zbl 1071.11508
Tate, John
1995
On Stark’s conjectures on the behavior of $$L(s,\chi)$$ at $$s=0$$. Zbl 0514.12013
Tate, John
1981
Rigid analytic spaces. Zbl 0208.48301
Tate, J.
1962
Local constants. (Prepared in collaboration with C. J. Bushnell and M. J. Taylor.). Zbl 0425.12019
Tate, J. T.
1977
Finite flat group schemes. Zbl 0924.14024
Tate, John
1997
Brumer-Stark-Stickelberger. Zbl 0504.12005
Tate, John
1981
On Chevalley’s proof of Lüroth’s theorem. Zbl 0047.03802
Lang, Serge; Tate, John
1952
Refining Gross’s conjecture on the values of abelian $$L$$-functions. Zbl 1072.11087
Tate, John
2004
Linear forms in $$\mathfrak p$$-adic roots of unity. Zbl 0893.11015
Tate, John; Voloch, José Felipe
1996
Letter from Tate to Iwasawa on a relation between $$K_2$$ and Galois cohomology. Zbl 0284.12004
Tate, J.
1973
On the inequality of Castelnuovo-Severi. Zbl 0081.37604
Mattuck, Arthur; Tate, John
1958
The centers of 3-dimensional Sklyanin algebras. Zbl 0823.17019
Artin, Michael; Schelter, William; Tate, John
1994
Abelian varieties isogenous to a power of an elliptic curve. Zbl 1400.14116
Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T.
2018
Ramification groups of local fields. Zbl 0136.02702
Sen, Shankar; Tate, John
1963
Classes d’isogénie des variétés abéliennes sur un corps fini. Zbl 0212.25703
Tate, John
1970
Algebraic cohomology classes. Translated by Yu. I. Manin. Zbl 0213.22901
Tate, John
1965
Galois cohomology. Zbl 1030.11060
Tate, John
2001
Arithmetic and geometry. Papers dedicated to I. R. Shafarevich on the occasion of his sixtieth birthday. Vol. I: Arithmetic. Zbl 0518.00004
Artin, Michael (ed.); Tate, John (ed.)
1983
On the Galois cohomology of unramified extensions of function fields in one variable. Zbl 0068.03402
1955
Alexandre Grothendieck 1928–2014, part 2. Zbl 1338.01023
Artin, Michael (ed.); Jackson, Allyn (ed.); Mumford, David (ed.); Tate, John (ed.); Ladegaillerie, Yves; Lichtenbaum, Stephen; Lochak, Pierre; Mazur, Barry; Messing, William; Murre, Jacob; Schneps, Leila
2016
Alexandre Grothendieck 1928–2014. I. Zbl 1338.01022
Artin, Michael (ed.); Jackson, Allyn (ed.); Mumford, David (ed.); Tate, John (ed.); Atiyah, Michael; Bass, Hyman; Cartier, Pierre; Deligne, Pierre; Demazure, Michel; Greenberg, Marvin Jay; Hartshorne, Robin; Illusie, Luc; Katz, Nicholas; Kleiman, Steven L.
2016
Autobiography. Zbl 1317.01039
Tate, John
2014
Stark’s basic conjecture. Zbl 1263.11101
Tate, John
2011
Bernard Dwork (1923–1998). Zbl 1177.01050
Katz, Nicholas M.; Tate, John
1999
Fields Medals. IV: An instinct for the key idea. Zbl 1225.01080
Mumford, David; Tate, John
1978
On the torsion in $$K_2$$ of fields. Zbl 0368.12008
Tate, J.
1977
The work of David Mumford. Zbl 0333.01015
Tate, J.
1975
Group schemes of prime order. Zbl 0225.14024
Tate, John; Oort, Frans
1972
Good reduction of abelian varieties. Zbl 0217.05201
Serre, Jean-Pierre; Tate, J.
1971
Principal homogeneous spaces for abelian varieties. Zbl 0116.38201
Tate, J.
1962
On the relation between extremal points of convex sets and homomorphisms of algebras. Zbl 0043.11403
Tate, John
1951
Abelian varieties isogenous to a power of an elliptic curve. Zbl 1400.14116
Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T.
2018
Alexandre Grothendieck 1928–2014, part 2. Zbl 1338.01023
Artin, Michael (ed.); Jackson, Allyn (ed.); Mumford, David (ed.); Tate, John (ed.); Ladegaillerie, Yves; Lichtenbaum, Stephen; Lochak, Pierre; Mazur, Barry; Messing, William; Murre, Jacob; Schneps, Leila
2016
Alexandre Grothendieck 1928–2014. I. Zbl 1338.01022
Artin, Michael (ed.); Jackson, Allyn (ed.); Mumford, David (ed.); Tate, John (ed.); Atiyah, Michael; Bass, Hyman; Cartier, Pierre; Deligne, Pierre; Demazure, Michel; Greenberg, Marvin Jay; Hartshorne, Robin; Illusie, Luc; Katz, Nicholas; Kleiman, Steven L.
2016
Rational points on elliptic curves. 2nd ed. Zbl 1346.11001
Silverman, Joseph H.; Tate, John T.
2015
Autobiography. Zbl 1317.01039
Tate, John
2014
Stark’s basic conjecture. Zbl 1263.11101
Tate, John
2011
Class field theory. Reprint of the 1990 2nd ed. Zbl 1179.11040
Artin, Emil; Tate, John
2009
Computation of $$p$$-adic heights and log convergence. Zbl 1135.11034
Mazur, Barry; Stein, William; Tate, John
2007
On the Jacobians of plane cubics. Zbl 1092.14054
Artin, Michael; Rodriguez-Villegas, Fernando; Tate, John
2005
Refining Gross’s conjecture on the values of abelian $$L$$-functions. Zbl 1072.11087
Tate, John
2004
Galois cohomology. Zbl 1030.11060
Tate, John
2001
Bernard Dwork (1923–1998). Zbl 1177.01050
Katz, Nicholas M.; Tate, John
1999
Finite flat group schemes. Zbl 0924.14024
Tate, John
1997
Homological properties of Sklyanin algebras. Zbl 0876.17010
Tate, John; Van den Bergh, Michel
1996
Linear forms in $$\mathfrak p$$-adic roots of unity. Zbl 0893.11015
Tate, John; Voloch, José Felipe
1996
A review of non-Archimedean elliptic functions. Zbl 1071.11508
Tate, John
1995
Conjectures on algebraic cycles in $$\ell$$-adic cohomology. Zbl 0814.14009
Tate, John
1994
The non-existence of certain Galois extensions of $$\mathbb{Q}$$ unramified outside 2. Zbl 0814.11057
Tate, John
1994
The center of the $$3$$-dimensional and $$4$$-dimensional Sklyanin algebras. Zbl 0809.16053
Smith, S. P.; Tate, J.
1994
The centers of 3-dimensional Sklyanin algebras. Zbl 0823.17019
Artin, Michael; Schelter, William; Tate, John
1994
Rational points on elliptic curves. Zbl 0752.14034
Silverman, Joseph H.; Tate, John
1992
Modules over regular algebras of dimension 3. Zbl 0763.14001
Artin, M.; Tate, J.; Van den Bergh, M.
1991
Quantum deformations of $$\text{GL}_ n$$. Zbl 0753.17015
Artin, Michael; Schelter, William; Tate, John
1991
The $$p$$-adic sigma function. Zbl 0735.14020
Mazur, B.; Tate, J.
1991
Some algebras associated to automorphisms of elliptic curves. Zbl 0744.14024
Artin, M.; Tate, J.; Van den Bergh, M.
1990
Class field theory. 2nd ed. Zbl 0681.12003
Artin, Emil; Tate, John
1990
Refined conjectures of the “Birch and Swinnerton-Dyer type”. Zbl 0636.14004
Mazur, B.; Tate, J.
1987
On $$p$$-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Zbl 0699.14028
Mazur, B.; Tate, J.; Teitelbaum, J.
1986
The Stark conjectures on Artin $$L$$-functions at $$s=0$$. Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher. Zbl 0545.12009
Tate, John
1984
Canonical height pairings via biextensions. Zbl 0574.14036
Mazur, B.; Tate, J.
1983
A reciprocity law for $$K_2$$-traces. Zbl 0514.18010
Rosset, Shmuel; Tate, John
1983
Variation of the canonical height of a point depending on a parameter. Zbl 0618.14019
Tate, J.
1983
Arithmetic and geometry. Papers dedicated to I. R. Shafarevich on the occasion of his sixtieth birthday. Vol. I: Arithmetic. Zbl 0518.00004
Artin, Michael (ed.); Tate, John (ed.)
1983
On Stark’s conjectures on the behavior of $$L(s,\chi)$$ at $$s=0$$. Zbl 0514.12013
Tate, John
1981
Brumer-Stark-Stickelberger. Zbl 0504.12005
Tate, John
1981
Number theoretic background. Zbl 0422.12007
Tate, J.
1979
Fields Medals. IV: An instinct for the key idea. Zbl 1225.01080
Mumford, David; Tate, John
1978
Local constants. (Prepared in collaboration with C. J. Bushnell and M. J. Taylor.). Zbl 0425.12019
Tate, J. T.
1977
On the torsion in $$K_2$$ of fields. Zbl 0368.12008
Tate, J.
1977
Relations between $$K_2$$ and Galois cohomology. Zbl 0359.12011
Tate, John
1976
Algorithm for determining the type of a singular fiber in an elliptic pencil. Zbl 1214.14020
Tate, J.
1975
The work of David Mumford. Zbl 0333.01015
Tate, J.
1975
The arithmetic of elliptic curves. Zbl 0296.14018
Tate, John T.
1974
The Milnor ring of a global field. Zbl 0299.12013
Bass, H.; Tate, J.
1973
Points of order 13 on elliptic curves. Zbl 0268.14009
Mazur, B.; Tate, J.
1973
Letter from Tate to Iwasawa on a relation between $$K_2$$ and Galois cohomology. Zbl 0284.12004
Tate, J.
1973
Group schemes of prime order. Zbl 0225.14024
Tate, John; Oort, Frans
1972
Rigid analytic spaces. Zbl 0212.25601
Tate, J.
1971
Classes d’isogénie des variétés abéliennes sur un corps fini (d’après Z. Honda). Zbl 0212.25702
Tate, John
1971
Symbols in arithmetic. Zbl 0229.12013
Tate, John
1971
Good reduction of abelian varieties. Zbl 0217.05201
Serre, Jean-Pierre; Tate, J.
1971
Group schemes of prime order. Zbl 0195.50801
Tate, John; Oort, Frans
1970
Classes d’isogénie des variétés abéliennes sur un corps fini. Zbl 0212.25703
Tate, John
1970
Good reduction of abelian varieties. Zbl 0172.46101
Serre, Jean-Pierre; Tate, J.
1968
Class field theory. Zbl 0176.33504
Artin, Emil; Tate, John
1968
Residues of differentials on curves. Zbl 0159.22702
Tate, John
1968
$$p$$-divisible groups. Zbl 0157.27601
Tate, J. T.
1967
Global class field theory. Zbl 1179.11041
Tate, J. T.
1967
The rank of elliptic curves. Zbl 0168.42201
Tate, J. T.; Shafarevich, I. R.
1967
Endomorphisms of Abelian varieties over finite fields. Zbl 0147.20303
Tate, J.
1966
Formal moduli for one-parameter formal Lie groups. Zbl 0156.04105
Lubin, J.; Tate, J.
1966
On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. Zbl 0199.55604
Tate, John
1966
The cohomology groups of tori in finite Galois extensions of number fields. Zbl 0146.06501
Tate, J.
1966
Formal complex multiplication in local fields. Zbl 0128.26501
Lubin, Jonathan; Tate, John
1965
Algebraic cycles and poles of zeta functions. Zbl 0213.22804
Tate, John T.
1965
Algebraic cohomology classes. Translated by Yu. I. Manin. Zbl 0213.22901
Tate, John
1965
Nilpotent quotient groups. Zbl 0125.01503
Tate, J.
1964
Duality theorems in Galois cohomology over number fields. Zbl 0126.07002
Tate, J.
1963
Ramification groups of local fields. Zbl 0136.02702
Sen, Shankar; Tate, John
1963
Rigid analytic spaces. Zbl 0208.48301
Tate, J.
1962
Principal homogeneous spaces for abelian varieties. Zbl 0116.38201
Tate, J.
1962
Principal homogeneous spaces over Abelian varieties. Zbl 0097.36203
Lang, Serge; Tate, John
1958
WC-groups over $$p$$-adic fields. Zbl 0091.33701
Tate, J.
1958
On the inequality of Castelnuovo-Severi. Zbl 0081.37604
Mattuck, Arthur; Tate, John
1958
Homology of Noetherian rings and local rings. Zbl 0079.05501
Tate, John
1957
On the characters of finite groups. Zbl 0065.01401
Brauer, Richard; Tate, John
1955
On the Galois cohomology of unramified extensions of function fields in one variable. Zbl 0068.03402
1955
Genus change in inseparable extensions of function fields. Zbl 0047.03901
Tate, John
1952
The higher dimensional cohomology groups of class field theory. Zbl 0047.03703
Tate, John
1952
On Chevalley’s proof of Lüroth’s theorem. Zbl 0047.03802
Lang, Serge; Tate, John
1952
A note on finite ring extensions. Zbl 0043.26701
Artin, Emil; Tate, John T.
1951
On the relation between extremal points of convex sets and homomorphisms of algebras. Zbl 0043.11403
Tate, John
1951
all top 5

#### Cited by 2,522 Authors

 26 Zarkhin, Yuriĭ Gennad’evich 24 Mazur, Barry 22 Zhang, James J. 21 Shioda, Tetsuji 21 Smith, S. Paul 18 Van den Bergh, Michel 17 Vancliff, Michaela 16 Rubin, Karl Cooper 15 Gross, Benedict Hyman 14 Pablos Romo, Fernando 13 Qin, Hourong 13 Tate, John Torrence jun. 12 Avramov, Luchezar L. 12 Banaszak, Grzegorz 12 Fein, Burton 12 Oort, Frans 12 Perrin-Riou, Bernadette 12 Schacher, Murray M. 12 Silverman, Joseph Hillel 11 Bosch, Siegfried 11 Stafford, J. Toby 11 Ulmer, Douglas L. 10 Darmon, Henri René 10 Kamienny, Sheldon 10 Mori, Izuru 10 Rogalski, Daniel 10 Schütt, Matthias 10 Virdol, Cristian 9 de Shalit, Ehud 9 Kato, Kazuya 9 Lütkebohmert, Werner 9 Milne, James Stuart 9 Morrison, David R. 9 Rump, Wolfgang 9 Silverberg, Alice 9 Tamagawa, Akio 8 Artin, Michael 8 Bertolini, Massimo 8 Gras, Georges 8 Jaulent, Jean-François 8 Kahn, Bruno 8 Kramer, Kenneth B. 8 Le Bruyn, Lieven 8 Liedtke, Christian 8 Lorenzini, Dino J. 8 Miao, Long 8 Nguyen Quang Do, Thong 8 Okniński, Jan 8 Opolka, Hans 8 Popescu, Cristian D. 8 Sands, Jonathan W. 8 Sierra, Susan J. 8 Tafazolian, Saeed 8 Top, Jaap 8 Yu, Chia-Fu 7 Chan, Daniel 7 Coates, John H. 7 Coleman, Robert Frederick 7 Greither, Cornelius 7 Hartl, Urs T. 7 Hida, Haruzo 7 Jespers, Eric 7 Kirkman, Ellen E. 7 Kolster, Manfred 7 Kraus, Alain 7 Li, Shirong 7 Mináč, Ján 7 Nickel, Andreas 7 Raynaud, Michel 7 Roblot, Xavier-François 7 Rohrlich, David E. 7 Stein, William A. 7 Stöhr, Karl-Otto 7 Torres, Fernando 7 Walton, Chelsea 7 Xu, Kejian 6 Assim, Jilali 6 Balakrishnan, Jennifer S. 6 Bloch, Spencer J. 6 Boxall, John L. 6 Brumer, Armand 6 Burns, David John 6 Cassidy, Thomas 6 Chirvăsitu, Alexandru 6 Choudhry, Ajai 6 Dokchitser, Vladimir 6 Fisher, Tom A. 6 Frey, Gerhard 6 Gateva-Ivanova, Tatiana 6 Herzog, Jürgen 6 Iyengar, Srikanth B. 6 Jones, John William 6 Katz, Nicholas Michael 6 Kurihara, Masato 6 Lei, Antonio 6 Li, Hua-Chieh 6 Longhi, Ignazio 6 Movahhedi, Abbas 6 Pollack, Robert 6 Rehmann, Ulf ...and 2,422 more Authors
all top 5

#### Cited in 255 Serials

 286 Journal of Number Theory 249 Journal of Algebra 177 Inventiones Mathematicae 132 Compositio Mathematica 128 Journal of Pure and Applied Algebra 115 Transactions of the American Mathematical Society 105 Mathematische Annalen 103 Duke Mathematical Journal 81 Communications in Algebra 81 Mathematische Zeitschrift 67 Journal de Théorie des Nombres de Bordeaux 60 Advances in Mathematics 60 Proceedings of the American Mathematical Society 59 Manuscripta Mathematica 55 Annales de l’Institut Fourier 47 Mathematics of Computation 41 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 37 Israel Journal of Mathematics 37 Journal of High Energy Physics 34 Archiv der Mathematik 33 Journal für die Reine und Angewandte Mathematik 32 Proceedings of the Japan Academy. Series A 32 International Journal of Number Theory 29 Bulletin of the American Mathematical Society. New Series 24 Tohoku Mathematical Journal. Second Series 24 Annals of Mathematics. Second Series 22 Rocky Mountain Journal of Mathematics 21 Nagoya Mathematical Journal 18 Bulletin de la Société Mathématique de France 18 $$K$$-Theory 18 Journal of the American Mathematical Society 18 Finite Fields and their Applications 18 Comptes Rendus. Mathématique. Académie des Sciences, Paris 17 Algebras and Representation Theory 17 Bulletin of the American Mathematical Society 16 Publications Mathématiques 16 Journal of Mathematical Sciences (New York) 15 Communications in Mathematical Physics 15 Documenta Mathematica 14 Journal of Soviet Mathematics 13 Mathematical Proceedings of the Cambridge Philosophical Society 13 Acta Arithmetica 13 Functiones et Approximatio. Commentarii Mathematici 13 Glasgow Mathematical Journal 13 Journal of Algebraic Geometry 13 Research in Number Theory 12 Mathematical Notes 12 Experimental Mathematics 12 Annales Mathématiques du Québec 11 Algebra & Number Theory 10 Acta Mathematica Sinica. English Series 10 Bulletin de la Société Mathématique de France. Supplément. Mémoires 9 Bulletin of the Australian Mathematical Society 9 Nuclear Physics. B 9 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 9 Memoirs of the American Mathematical Society 9 Rendiconti del Seminario Matematico della Università di Padova 9 The Ramanujan Journal 9 Journal of Noncommutative Geometry 8 Journal of Geometry and Physics 8 Mathematische Nachrichten 8 Proceedings of the London Mathematical Society. Third Series 8 Tokyo Journal of Mathematics 8 Journal of Symbolic Computation 8 Selecta Mathematica. New Series 8 LMS Journal of Computation and Mathematics 8 Central European Journal of Mathematics 8 Journal of the Institute of Mathematics of Jussieu 8 Journal of Algebra and its Applications 8 Journal of Homotopy and Related Structures 8 Journal of $$K$$-Theory 8 European Journal of Mathematics 7 Michigan Mathematical Journal 7 Science in China. Series A 7 Linear Algebra and its Applications 7 Journal of the European Mathematical Society (JEMS) 7 Proceedings of the Steklov Institute of Mathematics 7 Science China. Mathematics 6 Bulletin of the London Mathematical Society 6 Pacific Journal of Mathematics 6 Topology and its Applications 6 Forum Mathematicum 6 Proceedings of the Japan Academy 6 Kyoto Journal of Mathematics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Functional Analysis and its Applications 5 Journal of the Mathematical Society of Japan 5 Mémoires de la Société Mathématique de France. Nouvelle Série 5 Vestnik St. Petersburg University. Mathematics 5 Annales Mathématiques Blaise Pascal 5 Research in the Mathematical Sciences 4 Letters in Mathematical Physics 4 Linear and Multilinear Algebra 4 Periodica Mathematica Hungarica 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Collectanea Mathematica 4 Kodai Mathematical Journal 4 Monatshefte für Mathematik 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University ...and 155 more Serials
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#### Cited in 53 Fields

 1,739 Number theory (11-XX) 1,414 Algebraic geometry (14-XX) 414 Associative rings and algebras (16-XX) 218 Group theory and generalizations (20-XX) 215 Commutative algebra (13-XX) 151 Field theory and polynomials (12-XX) 148 $$K$$-theory (19-XX) 118 Category theory; homological algebra (18-XX) 113 Nonassociative rings and algebras (17-XX) 97 Topological groups, Lie groups (22-XX) 86 Quantum theory (81-XX) 80 Algebraic topology (55-XX) 62 Several complex variables and analytic spaces (32-XX) 37 Linear and multilinear algebra; matrix theory (15-XX) 37 Information and communication theory, circuits (94-XX) 34 Dynamical systems and ergodic theory (37-XX) 33 Functional analysis (46-XX) 29 Differential geometry (53-XX) 29 Manifolds and cell complexes (57-XX) 25 Relativity and gravitational theory (83-XX) 20 Combinatorics (05-XX) 18 Global analysis, analysis on manifolds (58-XX) 17 Geometry (51-XX) 15 Computer science (68-XX) 14 History and biography (01-XX) 11 Abstract harmonic analysis (43-XX) 9 Convex and discrete geometry (52-XX) 8 Special functions (33-XX) 7 General and overarching topics; collections (00-XX) 7 Mathematical logic and foundations (03-XX) 7 Functions of a complex variable (30-XX) 6 Operator theory (47-XX) 5 General algebraic systems (08-XX) 4 Difference and functional equations (39-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Partial differential equations (35-XX) 2 General topology (54-XX) 2 Numerical analysis (65-XX) 2 Mechanics of particles and systems (70-XX) 2 Fluid mechanics (76-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 2 Mathematics education (97-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX)

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